Related papers: About exchanging expectation and supremum for cond…

Let $T:Y\to X$ be a bounded linear operator between two normed spaces. We characterize compactness of $T$ in terms of differentiability of the Lipschitz functions defined on $X$ with values in another normed space $Z$. Furthermore, using a…

We prove the existence of nonnegative weak solutions to a class of second and fourth order nonautonomous nonlinear evolution equations with an explicitly time-dependent mobility function posed on the whole space $\mathbb{R}^d$, for…

Wasserstein projections in the convex order were first considered in the framework of weak optimal transport, and found application in various problems such as concentration inequalities and martingale optimal transport. In dimension one,…

Evolutionary algorithms (EAs) serve as powerful black-box optimizers inspired by biological evolution. However, most existing EAs predominantly focus on heuristic operators such as crossover and mutation, while usually overlooking…

Being able to generate constrained samples is one of the most appealing applications of the deep generators. Conditional generators are one of the successful implementations of such models wherein the created samples are constrained to a…

We propose an approach to generate realistic and high-fidelity stock market data based on generative adversarial networks (GANs). Our Stock-GAN model employs a conditional Wasserstein GAN to capture history dependence of orders. The…

Deep networks are increasingly applied to a wide variety of data, including data with high-dimensional predictors. In such analysis, variable selection can be needed along with estimation/model building. Many of the existing deep network…

We present the first minimax risk bounds for estimators of the spectral measure in multivariate linear factor models, where observations are linear combinations of regularly varying latent factors. Non-asymptotic convergence rates are…

It has long been thought that high-dimensional data encountered in many practical machine learning tasks have low-dimensional structure, i.e., the manifold hypothesis holds. A natural question, thus, is to estimate the intrinsic dimension…

Wasserstein Generative Adversarial Networks (WGANs) provide a versatile class of models, which have attracted great attention in various applications. However, this framework has two main drawbacks: (i) Wasserstein-1 (or Earth-Mover)…

Summary]{In this paper, we study problems of minimization of a functional depending on the fractional Caputo derivative of order $0<\alpha \leq 1$ and the fractional Riemann- Liouville integral of order $\beta > 0$ at fixed endpoints. A…

Recent neural networks such as WaveNet and sampleRNN that learn directly from speech waveform samples have achieved very high-quality synthetic speech in terms of both naturalness and speaker similarity even in multi-speaker text-to-speech…

Recently, a Wasserstein analogue of the Cramer--Rao inequality has been developed using the Wasserstein information matrix (Otto metric). This inequality provides a lower bound on the Wasserstein variance of an estimator, which quantifies…

Statistical machine learning theory often tries to give generalization guarantees of machine learning models. Those models naturally underlie some fluctuation, as they are based on a data sample. If we were unlucky, and gathered a sample…

We show how to compute lower bounds for the supremum Bayes error if the class-conditional distributions must satisfy moment constraints, where the supremum is with respect to the unknown class-conditional distributions. Our approach makes…

Concentration inequalities are fundamental tools in probabilistic combinatorics and theoretical computer science for proving that random functions are near their means. Of particular importance is the case where f(X) is a function of…

We present Wasserstein introspective neural networks (WINN) that are both a generator and a discriminator within a single model. WINN provides a significant improvement over the recent introspective neural networks (INN) method by enhancing…

We consider a Laplacian on the one-sided full shift space over a finite symbol set, which is constructed as a renormalized limit of finite difference operators. We propose a weak definition of this Laplacian, analogous to the one in…

In this paper, we investigate the training process of generative networks that use a type of probability density distance named particle-based distance as the objective function, e.g. MMD GAN, Cram\'er GAN, EIEG GAN. However, these GANs…

We prove bounds for the truncated directional Hilbert transform in $L^p(\mathbb{R}^2)$ for any $1<p<\infty$ under a combination of a Lipschitz assumption and a lacunarity assumption. It is known that a lacunarity assumption alone is not…